Superquadratic function and its applications in information theory via interval calculus

Saad Ihsan Butt and Dawood Khan

Chaos, Solitons & Fractals, 2025, vol. 190, issue C

Abstract: The goal of this study is to introduce a new class of superquadraticity, which is known as superquadratic interval valued function (superquadratic I-V-F) and establish its properties via order relations of intervals. By utilizing the definitions and properties of superquadratic I-V-F, we come up with new integral inequalities such that Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite–Hadamard types. In addition to this, we provide a fractional version of Hermite–Hadamard’s type inequalities for superquadratic I-V-Fs. The findings are validated by specific numerical computations and graphical illustrations that include a certain number of relevant examples. We also offer the applications of the established results in information theory such that we determine the novel estimates for Shannon’s and relative entropies.

Keywords: Superquadratic I-V-F; Jensen’s inequality; Fractional calculus; Shannon entropy; Hermite–Hadamard’s inequality; Relative entropy (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924013006

DOI: 10.1016/j.chaos.2024.115748

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